What we do
Probability & Stochastic Models
We have interests in both the development of new theoretical ideas and techniques within the realm of probability and stochastic models and the applications of probabilistic ideas to tackle novel problems within the real world. This has included research into:
- theoretical areas of limit theorems
- stability theory
- stochastic dynamics
- random combinatorial structures
- stochastic analysis
- random walks, etc.
In addition the group has a strong interest in problems of a stochastic nature which arise from the realms of communication and power systems. This leads the group to carry an active research programme in:
- stochastic networks
- queuing theory and probabilistic analysis of algorithms
- mathematical finance
- risk analysis
The probability group has long-term close contacts with many leading centres of research within UK (universities of Cambridge, Oxford, Edinburgh, Strathclyde, and others) and abroad (ENS/INRIA, EURANDOM, universities of Stanford, Novosibirsk, etc.) Our group collaborates with various other research teams within the university, including those in Schools of Life Sciences and Petroleum Engineering. In addition, strong ties are nurtured with industry, which include National Grid Plc., Scottish and Southern Energy.
Our work spans classical and Bayesian methods, the development of theory and the application of new methods in numerous areas. In epidemiology the group has a long history of developing techniques for fitting and testing stochastic dynamical models for spatio-temporal spread of epidemics using typically sparse data. Recent applications have covered the spread of virus and bacterial diseases of citrus, as well as economically important pathogens of animals and humans such as FMD, SARS and MRSA. More generally the group has collaborated with scientists from a range of disciplines in applying bayesian methods to problems arising in laser imaging, modelling of diabetes symptom reporting, and failure of drainage systems. The group also has a strong track record in classical techniques. Recent examples include the development of spline-based methodology for smoothing mortality data and the use of classical filtering techniques to build fast emulators for complex building simulation models.
Within the university we collaborate with colleagues in the School of Engineering and Physical Sciences and the School of Built Environment. We have strong links with the Department of Plant Sciences at Cambridge University, and internationally with Queensland University of Technology and the University of Leiden.
Numerics for SDEs & SPDEs
We have expertise on the analysis and implementation of numerical schemes for both stochastic differential equations and stochastic partial differential equations. This includes work on strong convergence of numerical methods, geometric and exponential integrators, positivity preserving, space-time adaptivity and multi-level Monte-Carlo methods. We have been interested in systems that arise in finance, computational neuroscience and porous media.
Stochastic Systems Laboratory
The aim of the Laboratory is to facilitate both research and knowledge transfer. Important areas of application include energy, transport and communications networks. In depth details can be found on the Stochastic Systems Laboratory page.